Intrinsic Spin and Polarization in Complementary Phase Geometry

Complementary Phase Geometry (CPG) contains an intrinsic three-dimensional complementary rotational sector. Here this structure is examined as a geometric carrier of spin and polarization. A normalized complementary rotation bivector defines an oriented plane whose dual axis is identified with polarization. Its spinorial lift yields the standard double-cover structure $Spin(3)\\simeq SU(2)$ and the half-phase relation $\\chi^2=\\Upsilon$. In the fundamental representation,\\[ \\hat S_a=\\frac{b}{2}\\sigma_a,\\]where $b$ is the CPG action scale; with the empirical identification $b=\\hbar$, the standard spin-$1/2$ algebra, projections, and Casimir are recovered. Combining the polarization--plane identification with the pre-existing mixed observable--complementary dynamics of CPG yields a further conditional prediction. Both the free-flight timing variance and the transverse-position variance contain the common dimensionless dependence\\[ \\sin^2\\vartheta\\, \\sin^2\\!\\left( \\frac{\\omega_{\\rm M}L}{2v} \\right),\\]while their dimensional prefactors are different. When the rapid propagation phase is unresolved, the common angular dependence reduces to $\\sin^2\\vartheta$. The absolute magnitudes remain controlled by presently undetermined complementary and mixed-coupling parameters. Phenomenological magnetic coupling reproduces standard Stern--Gerlach eigenchannels and analyzer-overlap weights. Magnetic moments, microscopic branch selection, and Born-rule statistics remain open.